3. a) Write the equations of motion for a bi-dimensional square lattice formed by equal atoms, with mass m, connected by
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3. a) Write the equations of motion for a bi-dimensional square lattice formed by equal atoms, with mass m, connected by
3. a) Write the equations of motion for a bi-dimensional square lattice formed by equal atoms, with mass m, connected by springs of spring constant k. (Draw a picture of the system and explain each of the potential terms. Explain all the math passages and show the complete solution) b) A particle of mass m is under the action of a force whose potential energy is: V = ax2-bx3 = 1) Determine the strength. II) The particle starts at the origin x=0 with speed Vo. Show that if the modulus of VO is less than Vcl Vol <Vc), where Vc is a certain critical velocity, the particle will remain confined to the region close to the origin. Determine V. (Graph the function V(x), determine the maximums and minimums, and analyze the limits for x tending to infinity and x tending to zero)
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